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BEGIN:VEVENT
SUMMARY:Classical and Restricted Impulse Control for the Exchange Rate und
er Incomplete Knowledge of the Model
DTSTART;VALUE=DATE-TIME:20180829T142000Z
DTEND;VALUE=DATE-TIME:20180829T145000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3136@indico.math.cnrs.fr
DESCRIPTION:Speakers: Wolfgang Runggaldier (University of Padova\, Italy)\
nABSTRACT: We consider the problem faced by a Central Bank of optimally\nc
ontrolling the exchange rate over a finite time horizon\, whereby it can u
se\ntwo non-excluding tools: controlling directly the exchange rate in the
\nform of an impulse control\; controlling it indirectly via the domestic\
nexchange rate in the form of a continuously acting control. In line\nwith
existing literature we consider this as a mixed\nclassical-impulse contro
l problem for which\, on the basis of a\nquasi-variational inequality\, we
search for an analytic solution within a\nspecific class of value functio
ns and controls. Besides the finite\nhorizon\, the main novelty here is th
e assumption that the drift in the\nexchange rate dynamics is not directly
observable and has thus to be\nfilter-estimated from observable data. The
problem becomes thus time\ninhomogeneous and the Markovian state variable
s have to include also\nthe filter of the drift. This is a joint work with
\n> Kazuhiro Yasuda.\n\nhttps://indico.math.cnrs.fr/event/3123/contributi
ons/3136/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimal financing and investment strategies under asymmetric infor
mation about collateral value
DTSTART;VALUE=DATE-TIME:20180830T103000Z
DTEND;VALUE=DATE-TIME:20180830T110000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3137@indico.math.cnrs.fr
DESCRIPTION:Speakers: Takashi Shibata (Tokyo Metropolitan University)\nWe
examine the interactions between financing (capital structure) and investm
ent decisions of a firm under asymmetric information about collateral (liq
uidation) value between well-informed managers and less-informed investors
. We show that asymmetric information reduces the amount of debt issuance
to finance the cost of investment\, that leads to delay corporate investme
nt. In particular\, an increase in the degree of asymmetric information fo
rces the firm to be a risk-free debt-equity financing (ultimately be the
all-equity financing) by reducing the amount of debt issuance. In addition
\, an increase in the cash flow volatility decreases the amount of debt is
suance\, credit spread\, and leverage under asymmetric information. Our re
sults fit well with empirical studies. This is a joint work with Michi Nis
hihara.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3137/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mass-Conserving Stochastic Partial Differential Equations and Rela
ted Backward Doubly Stochastic Differential Equations
DTSTART;VALUE=DATE-TIME:20180830T075000Z
DTEND;VALUE=DATE-TIME:20180830T082000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3138@indico.math.cnrs.fr
DESCRIPTION:Speakers: Qi Zhang (Fudan University)\nIn this talk\, i will i
ntroduce a type of mass-conserving stochastic partial differential equatio
ns which can be connected with a type of mass-conserving backward doubly s
tochastic differential equations. The Poincare’s inequality is used in t
he estimates to relax the monotonic condition of backward doubly stochasti
c differential equations.\n\nhttps://indico.math.cnrs.fr/event/3123/contri
butions/3138/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Fairness of Systemic Risk Measures
DTSTART;VALUE=DATE-TIME:20180830T063000Z
DTEND;VALUE=DATE-TIME:20180830T071000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3139@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marco Frittelli (Milano University)\nIn our previous
paper\, we have introduced a general class of systemic risk measures that
allow random allocations to individual banks before aggregation of their
risks. In the present paper\, we address the question of fairness of these
allocations and we propose a fair allocation of the total risk to individ
ual banks. We show that the dual problem of the minimization problem which
identify the systemic risk measure\, provides a valuation of the random a
llocations which is fair both from the point of view of the society/regula
tor and from the individual financial institutions. The case with exponent
ial utilities which allows for explicit computation is treated in details.
\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3139/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Entropy and additional utility of a discrete information disclosed
progressively in time
DTSTART;VALUE=DATE-TIME:20180828T140000Z
DTEND;VALUE=DATE-TIME:20180828T143000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3140@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anna Aksamit (University of Sydney)\nThe additional
information carried by enlarged filtration and its measurement was studied
by several authors. Already Meyer (Sur un theoreme de J. Jacod\, 1978) an
d Yor (Entropie d'une partition\, et grossissement initial d'une filtratio
n\, 1985)\, investigated stability of martingale spaces with respect to in
itial enlargement with atomic sigma-field. We extend these considerations
to the case where information is disclosed progressively in time. We defin
e the entropy of such information and we prove that its finiteness is enou
gh for stability of some martingale spaces in progressive setting. Finally
we calculate additional logarithmic utility of a discrete information dis
closed progressively in time.\n\nhttps://indico.math.cnrs.fr/event/3123/co
ntributions/3140/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Construction of an aggregate consistent utility\, without Pareto o
ptimality
DTSTART;VALUE=DATE-TIME:20180829T085000Z
DTEND;VALUE=DATE-TIME:20180829T092000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3141@indico.math.cnrs.fr
DESCRIPTION:Speakers: Caroline HILLAIRET (Ensae Paris tech\, CREST)\nThe a
im of this talk is to describe globally the behavior and preferences of h
eterogeneous agents. Our starting point is the aggregate wealth of a given
economy\, with a given repartition of the wealth among investors\, which
is not necessarily Pareto optimal.\nWe propose a construction of an aggreg
ate forward utility\, market consistent\,\nthat aggregates the marginal ut
ility of the heterogeneous agents. This construction\nis based on the aggr
egation of the pricing kernels of each investor. As an application\nwe ana
lyze the impact of the heterogeneity and of the wealth market on the yield
curve.\n\nThis is a joint work with Nicole El Karoui and Mohamed Mrad.\n\
nhttps://indico.math.cnrs.fr/event/3123/contributions/3141/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the conditions on pricing functional and trading strategies in
insider trading model
DTSTART;VALUE=DATE-TIME:20180830T092000Z
DTEND;VALUE=DATE-TIME:20180830T095000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3142@indico.math.cnrs.fr
DESCRIPTION:Speakers: Albina Danilova (LSE)\nIn this talk I will present s
ome "folk" results in insider trading literature. In particular\, I will d
iscuss conditions on pricing functional that are necessary for existence o
f equilibrium\, as well as the ones that are necessary for existence of *i
nconspicuous* equilibrium. I will prove that one can restrict insider trad
ing strategies to absolutely continuous ones.\n\nhttps://indico.math.cnrs.
fr/event/3123/contributions/3142/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Continuous-Time Constrained Stochastic Linear-Quadratic Control wi
th Financial Applications
DTSTART;VALUE=DATE-TIME:20180829T153000Z
DTEND;VALUE=DATE-TIME:20180829T160000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3144@indico.math.cnrs.fr
DESCRIPTION:Speakers: Xun LI (HK PolyU)\nThis work studies a class of cont
inuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control
problem with the linear control constraints. Using the state separation th
eorem induced from its special structure\, we derive the analytical soluti
on for this class of problem. The revealed optimal control policy is a pie
ce-wise affine function of system state. This control policy can be comput
ed efficiently by solving two Riccati equations off-line. Under some mild
conditions\, the stationary optimal control policy can be also achieved fo
r this class of problem with infinite horizon. This result can be applied
to solve the constrained dynamic mean-variance portfolio selection problem
. Examples shed light on the solution procedure of implementing our method
.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3144/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Stefan-type Problems and Order Book Dynamics
DTSTART;VALUE=DATE-TIME:20180828T092000Z
DTEND;VALUE=DATE-TIME:20180828T095000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3145@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marvin Mueller (ETH Zurich)\nMoving boundary problem
s allow to model macroscopic systems with phase transition at an inner bou
ndary. Motivated by problems in economics and finance\, more explicitely p
rice-time continuous modelling of the limit order book\, we consider a sto
chastic and non-linear extension of the classical Stefan-problem in one sp
ace dimension. More precisely\, the dynamics on buy and sell side in an el
ectronic financial markets are modeled by respective second order stochast
ic partial differential equations which are separated by an inner interfac
e: the mid-price. We discuss new results beyond existence theory\, such as
approximations of the solution.\n\nhttps://indico.math.cnrs.fr/event/3123
/contributions/3145/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mixed Deterministic and Random Optimal Control of Linear Stochasti
c Systems with Quadratic Costs
DTSTART;VALUE=DATE-TIME:20180829T124000Z
DTEND;VALUE=DATE-TIME:20180829T132000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3146@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shanjian Tang (Fudan University\, School of Mathemat
ical Science)\nWe consider the mixed optimal control of a linear stochasti
c system with a quadratic cost functional\, with two controllers---one can
choose only deterministic time functions\, called the deterministic contr
oller\, while the other can choose adapted random processes\, called the r
andom controller. The optimal control is shown to exist under suitable ass
umptions. The optimal control is characterized via a system of fully coup
led forward-backward stochastic differential equations (FBSDEs) of mean-fi
eld type. We solve the FBSDEs via solutions of two (but decoupled) Riccati
equations\, and give the respective optimal feedback law for both determi
nistic and random controllers\, using solutions of both Riccati equations.
The optimal state satisfies a linear stochastic differential equation (SD
E) of mean-field type. Both the singular and infinite time-horizonal cases
are also addressed. \n\nThis is a joint work with Ying HU\, Universite de
Rennes 1.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3146/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic control under periodic observation times
DTSTART;VALUE=DATE-TIME:20180831T085000Z
DTEND;VALUE=DATE-TIME:20180831T092000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3148@indico.math.cnrs.fr
DESCRIPTION:Speakers: Kazutoshi Yamazaki (Kansai University)\nWe consider
a version of the stochastic control problem\, in which control opportuniti
es arrive only at the jump times of an independent Poisson process. We con
sider perpetual American options\, optimal dividend problems\, and invento
ry control problems\, driven by a spectrally one-sided Levy process. In p
articular\, we show that barrier-type strategies are optimal under suitabl
e conditions. The optimal strategies and value functions are concisely wri
tten in terms of the scale functions. This talk is based on the joint work
with A. Bensoussan and J.L. Perez.\n\nhttps://indico.math.cnrs.fr/event/3
123/contributions/3148/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Skorokhod embedding problem and single jump martingales: a con
nection via change of time
DTSTART;VALUE=DATE-TIME:20180828T151000Z
DTEND;VALUE=DATE-TIME:20180828T154000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3149@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Gushchin (Steklov Mathematical Institute)\
nLet $\\overline N_t = \\sup_{s\\leq t} N_s$ be a running maximum of a loc
al martingale $N$. We assume that $N$ is max-continuous\, i.e. $\\overline
N$ is continuous. The Skorokhod embedding problem corresponds to a specia
l case where $N$ is a Brownian motion stopped at a finite stopping time $\
\tau$. Consider the change of time generated by the running maximum:\n $\n
\\sigma_t:=\\inf\\\,\\{s\\colon \\overline N_s>t\\}.\n $\n Then the time-
changed process $M:=N\\circ\\sigma$ has a simple structure:\n $\n M_t=N_{\
\sigma_t}= t\\wedge W - V1_{\\{t\\geq W\\}}\,\n $\n where $W:=\\overline N
_\\infty$ and $V:=\\overline N_\\infty-N_\\infty$ ($V$ is correctly define
d on the set $\\{\\overline N_\\infty < \\infty\\}$). Besides\, $M_\\infty
=N_\\infty$ and $\\overline M_\\infty=\\overline N_\\infty$. This simple o
bservation explains how we can use single jump martingales $M$ of the abov
e form to describe properties of $N$. For example\, $N$ is a closed superm
artingale if and only $M$ is a martingale and the negative part of $W-V$ i
s integrable. Another example shows how to connect the Dubins-Gilat constr
uction of a martingale whose supremum is given by the Hardy-Littlewood max
imal function and the Azéma-Yor construction in the Skorokhod embedding p
roblem.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3149/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nonparametric Bayesian volatility estimation
DTSTART;VALUE=DATE-TIME:20180830T100000Z
DTEND;VALUE=DATE-TIME:20180830T103000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3150@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Spreij (Korteweg-de Vries Institute for Mathem
atics\, Universiteit van Amsterdam)\nGiven discrete time observations over
a fixed time interval\, we study a nonparametric Bayesian approach to est
imation of the volatility coefficient of a stochastic differential equatio
n. We postulate a histogram-type prior on the volatility with piecewise co
nstant realisations on bins forming a partition of the time interval. The
values on the bins are assigned an inverse Gamma Markov chain (IGMC) prio
r. Posterior inference is straightforward to implement via Gibbs sampling\
, as the full conditional distributions are available explicitly and turn
out to be inverse Gamma. We also discuss in detail the hyperparameter sele
ction for our method. Our nonparametric Bayesian approach leads to good pr
actical results in representative simulation examples. Finally\, we apply
it on a classical data set in change-point analysis: weekly closings of th
e Dow-Jones industrial averages. [Joint work with Shota Gugushvili\, Morit
z Schauer and Frank van der Meulen.]\n\nhttps://indico.math.cnrs.fr/event/
3123/contributions/3150/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:BSDE formulation of combined regular and singular stochastic contr
ol problems
DTSTART;VALUE=DATE-TIME:20180831T120000Z
DTEND;VALUE=DATE-TIME:20180831T123000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3151@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ying Hu (University of Rennes 1)\nIn this talk\, we
study a class of combined regular and singular stochastic control problems
that can be expressed as constrained BSDEs. In the Markovian case\, this
reduces to a characterization through a PDE with gradient constraint. But
the BSDE formulation makes it possible to move beyond Markovian models and
consider path-dependent problems. We also provide an approximation of the
original control problem with standard BSDEs that yield a characterizatio
n of approximately optimal values and controls.\nThis is a joint work with
Bruno Bouchard and Patrick Cheridito.\n\nhttps://indico.math.cnrs.fr/even
t/3123/contributions/3151/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esscher pricing under progressive enlargement of information
DTSTART;VALUE=DATE-TIME:20180829T074000Z
DTEND;VALUE=DATE-TIME:20180829T082000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3152@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tahir Choulli (UNiversity of Alberta)\nWe investigat
e the Esscher pricing rule and the Esscher prices\, when the ``public" flo
w information denoted by $\\mathbb F$ is progressively enlarged by a rando
m time $\\tau$\, for both discrete-time and continuous-time settings. $\\t
au$ can represent the death time of an agent\, default time of a firm\, or
more generally the occurrence time of an even that might impact the marke
t somehow. Thus\, by considering the new flow of information $\\mathbb G$
resulting from the expansion of the flow $\\mathbb F$ with $\\tau$\, we ad
dress the stopped model $(S^{\\tau}$\,$\\mathbb{G})$ in different directi
ons and various frameworks. In discrete time\, for instance\, we describe
the Esscher martingale measure for the general case in different manners\,
and we illustrate the results on particular cases of models for the pair
$(S\,\\tau)$. To well illustrate the impact of $\\tau$ on the Esscher pri
cing rules and/or prices\, we consider the Black-Scholes model for $S$ and
a class of models for $\\tau$. For these models\, we describe the Esscher
martingale measures\, the Esscher prices for some death-linked contracts\
, the Greeks of these obtained Esscher prices\, and we compare the Esscher
prices with the Black-Scholes pricing formula. This talk is based on join
t work with Haya Alsemary (University of Alberta).\n\nhttps://indico.math.
cnrs.fr/event/3123/contributions/3152/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Can old-age provision benefit from recent developments in quantita
tive finance?
DTSTART;VALUE=DATE-TIME:20180830T085000Z
DTEND;VALUE=DATE-TIME:20180830T092000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3154@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Schmutz (University of Berne)\nAmong other f
actors\, the difficult market environment with its sustained low interest
rates triggers certain adjustments of investment and product strategies of
life insurance companies and pension funds. In this context\, the role of
life insurance companies and pension funds as long-term investors has inc
reasingly been discussed among the industry and financial market superviso
ry authorities. These discussions are often focused on the idea of trying
to benefit from the possibility of long-term hold to maturity strategies p
artially based on assets providing a certain illiquidity premium. This ide
a is compared to alternative ideas regarding investment or resolution plan
s for life insurance portfolios\, some of which are based on recent develo
pments in quantitative finance. Furthermore\, the link between investment
plans and product design will also be briefly discussed.\n\nhttps://indico
.math.cnrs.fr/event/3123/contributions/3154/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exact spectral asymptotics of fractional processes with applicatio
ns to inference
DTSTART;VALUE=DATE-TIME:20180828T095000Z
DTEND;VALUE=DATE-TIME:20180828T102000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3155@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marina Kleptsyna (Université du Maine)\nMany proble
ms of statistical inference can be solved\, using spectral decomposition\n
of stochastic processes. The principal difficulty with this approach is th
at eigenproblems\nare notoriously hard to solve in a reasonably explicit f
orm. In this talk I will survey some\nrecent results on the exact asymptot
ics in eigenproblems for fractional processes and\ndiscuss their applicati
ons to parameter estimation and filtering.\n\nhttps://indico.math.cnrs.fr/
event/3123/contributions/3155/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some existence and uniqueness results for obliquely reflected BSDE
s
DTSTART;VALUE=DATE-TIME:20180831T123000Z
DTEND;VALUE=DATE-TIME:20180831T130000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3156@indico.math.cnrs.fr
DESCRIPTION:Speakers: Adrien Richou (IMB - Université de Bordeaux)\nIn th
is talk\, we present some recent results on obliquely reflected BSDEs. In
particular we are able to deal with assumptions on the generator weaker th
an in currently known results. An existence and uniqueness result is obtai
ned in a non Markovian framework by assuming some regularity on the termin
al condition. Moreover\, a general existence result is obtained in the Mar
kovian framework. We also present an application to some new optimal switc
hing problems called randomised switching problems.\nThis is a joint work
with Jean-François Chassagneux (University of Paris 7)\n\nhttps://indico.
math.cnrs.fr/event/3123/contributions/3156/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantile optimization under derivative constraint
DTSTART;VALUE=DATE-TIME:20180831T151000Z
DTEND;VALUE=DATE-TIME:20180831T154000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3174@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zuoquan Xu (The Hong Kong Polytechnic University)\nT
his talk will focus on a new type of quantile optimization problems arisin
g\nfrom insurance contract design models. This type of optimization proble
ms is\ncharacterized by a constraint that the derivatives of the decision
quantile\nfunctions are bounded. Such a constraint essentially comes from
the\n“incentive compatibility” constraint for any optimal insurance co
ntract to\navoid the potential severe problem of moral hazard in insurance
contract\ndesign models. By a further development of the relaxation metho
d\, we\nprovide a systemic approach to solving this new type of quantile o
ptimization\nproblems. The optimal quantile is expressed via the solution
of a free\nboundary problem for a second-order nonlinear ordinary differen
tial equation\n(ODE)\, which is similar to the Black-Scholes ODE for perpe
tual American\noptions.\n\nhttps://indico.math.cnrs.fr/event/3123/contribu
tions/3174/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linear-Quadratic-Gaussian Mixed Games with Input Constraint Involv
ing Major Agent and Heterogeneous Minor Agents
DTSTART;VALUE=DATE-TIME:20180829T160000Z
DTEND;VALUE=DATE-TIME:20180829T163000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3175@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jianhui Huang (Hong kong Polytechnic University)\nWe
consider a class of linear-quadratic-Gaussian mean-field games with a maj
or agent and considerable heterogeneous minor agents with mean-field inter
actions. The individual admissible controls are constrained in closed conv
ex subsets of the full space. The decentralized strategies for individual
agents and the consistency condition system are represented in an unified
manner via a class of mean-field forward-backward stochastic differential
equation involving projection operators. The well-posedness of consistency
condition system is established and the related ε−Nash equilibrium pro
perty is also verified.\n\nhttps://indico.math.cnrs.fr/event/3123/contribu
tions/3175/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Infinite dimensional polynomial processes
DTSTART;VALUE=DATE-TIME:20180829T095000Z
DTEND;VALUE=DATE-TIME:20180829T102000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3176@indico.math.cnrs.fr
DESCRIPTION:Speakers: Christa Cuchiero (University of Vienna)\nMotivated f
rom high and infinite dimensional problems in mathematical finance\, we co
nsider infinite dimensional polynomial processes taking values in certain
space of measures or functions. We have two concrete applications in mind:
first\, modeling high or even potentially infinite dimensional financial
markets in a tractable and robust way\, and second analyzing stochastic Vo
lterra processes\, which recently gained popularity through rough volatili
ty models and ambit processes. The first question leads to probability mea
sure valued polynomial diffusions and the second one to Markovian lifts of
polynomial Volterra processes. For both cases we provide existence result
s and a moment formula.\n\nhttps://indico.math.cnrs.fr/event/3123/contribu
tions/3176/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalized Feller processes and Markovian lifts of stochastic Vol
terra processes: the affine case
DTSTART;VALUE=DATE-TIME:20180831T070000Z
DTEND;VALUE=DATE-TIME:20180831T074000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3177@indico.math.cnrs.fr
DESCRIPTION:Speakers: Josef Teichmann (ETH Zurich)\nWe consider stochastic
(partial) differential equations appearing as Markovian lifts of affine V
olterra processes with jumps from the point of view of the generalized Fel
ler property which was introduced in\, e.g.\, Dörsek-Teichmann (2010). In
particular we provide new existence\, uniqueness and approximation result
s for Markovian lifts of affine rough volatility models of general jump di
ffusion type. We demonstrate that in this Markovian light the theory of st
ochastic Volterra processes becomes almost classical.\n\nhttps://indico.ma
th.cnrs.fr/event/3123/contributions/3177/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Neumann Boundary Problem for Elliptic Partial Differential Equ
ations with Nonlinear Divergence Terms
DTSTART;VALUE=DATE-TIME:20180831T154000Z
DTEND;VALUE=DATE-TIME:20180831T161000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3178@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jing Zhang (Fudan University)\nWe prove the existenc
e and uniqueness of weak solution of a Neumann boundary problem for an ell
iptic partial differential equation (PDE for short) with a singular diver
gence term which can only be understood in a weak sense. A probabilistic a
pproach is applied by studying the backward stochastic differential equati
on (BSDE for short) corresponding to the PDE.\n\nhttps://indico.math.cnrs.
fr/event/3123/contributions/3178/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Double continuation regions for American and Swing options with ne
gative discount rate in Lévy models
DTSTART;VALUE=DATE-TIME:20180831T074000Z
DTEND;VALUE=DATE-TIME:20180831T082000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3179@indico.math.cnrs.fr
DESCRIPTION:Speakers: Zbigniew Palmowski (Wrocław University of Science a
nd Technology)\nIn this talk we\nanalyze perpetual American call and put o
ptions in an exponential L\\'evy model. \nWe consider a negative effective
discount rate which arises in a number of financial applications\nincludi
ng stock loans and real options\, where the strike price can potentially g
row at a higher rate than\nthe original discount factor. We show that in t
his case a double continuation region arises and we identify the two criti
cal prices. \nWe also generalize this result to multiple stopping problems
of swing type\, that is\, when\nsuccessive exercise opportunities are sep
arated by i.i.d. random\nrefraction times. We conduct numerical analysis f
or the Black-Scholes model and\nthe jump-diffusion model with exponentiall
y distributed jumps.\n\nhttps://indico.math.cnrs.fr/event/3123/contributio
ns/3179/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duality for homogeneous optimisation problems
DTSTART;VALUE=DATE-TIME:20180829T145000Z
DTEND;VALUE=DATE-TIME:20180829T152000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3180@indico.math.cnrs.fr
DESCRIPTION:Speakers: Michael Tehranchi (University of Cambridge)\nThis ta
lk is concerned with stochastic optimal control problems with a certain ho
mogeneity. For such problems\, a novel dual problem is formulated. The res
ults are applied to a stochastic volatility variant of the classical Merto
n problem. Another application of this duality is to the study the right-m
ost particle of a branching Levy process.\n\nhttps://indico.math.cnrs.fr/e
vent/3123/contributions/3180/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The asymptotic expansion of the regular discretization error of It
ô integrals
DTSTART;VALUE=DATE-TIME:20180828T085000Z
DTEND;VALUE=DATE-TIME:20180828T092000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3181@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Fukasawa (Osaka University)\nWe study a Edge
worth-type refinement of the central limit theorem for the discretizacion
error of Itô integrals. Towards this end\, we introduce a new approach\,
based on the anticipating I Itô formula. This alternative technique allow
s us to compute explicitly the terms of the corresponding expansion formul
a. A joint work with E. Alos.\n\nhttps://indico.math.cnrs.fr/event/3123/co
ntributions/3181/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representation of limit values for nonexpansive stochastic differe
ntial games
DTSTART;VALUE=DATE-TIME:20180831T143000Z
DTEND;VALUE=DATE-TIME:20180831T150000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3182@indico.math.cnrs.fr
DESCRIPTION:Speakers: Juan Li (Shandong University\, Weihai)\nA classical
problem in ergodic control theory consists in the study of the limit behav
iour of\nλV λ (·) as λ ↘ 0\, when V λ is the value function of a de
terministic or stochastic control problem\nwith discounted cost functional
with infinite time horizon and discount factor λ. We study this\nproblem
for the lower value function V λ of a stochastic differential game with
recursive cost\, i.e.\,\nthe cost functional is defined through a backward
stochastic differential equation with infinite\ntime horizon. But unlike
the ergodic control approach\, we are interested in the case where the\nli
mit can be a function depending on the initial condition. For this we exte
nd the so-called\nnon-expansivity assumption from the case of control prob
lems to that of stochastic differential\ngames.\nBased on a joint work wit
h Rainer Buckdahn (Brest\, France)\, Nana Zhao (Weihai\, China).\n\nhttps:
//indico.math.cnrs.fr/event/3123/contributions/3182/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the geometry of very rough Weierstrass curves: local time\, SBR
measure\, Hausdorff dimension
DTSTART;VALUE=DATE-TIME:20180830T071000Z
DTEND;VALUE=DATE-TIME:20180830T075000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3185@indico.math.cnrs.fr
DESCRIPTION:Speakers: Peter Imkeller (Mathematisches Institut der Humboldt
-Universität zu Berlin)\nWe investigate geometric properties of Weierstra
ss curves with two\ncomponents\, representing series based on trigonometri
c functions. They\nare seen to be 12 − Hölder continuous\, and are not
(para-)controlled\nwith respect to each other in the sense of the recently
established\nFourier analytic approach of rough path analysis. Their grap
h is rep-\nresented as an attractor of a smooth random dynamical system. F
or\none-dimensional versions we show existence of a local time and smooth-
\nness of the Sinai-Bowen-Ruelle (SBR) measure. Our argument that its\ngra
ph has Hausdorff dimension 2 is in the spirit of Ledrappier-Young’s\napp
roach of the Hausdorff dimension of attractors. This is joint work\nwith G
. dos Reis (U Edinburgh) and A. Réveillac (U Toulouse).\n\nhttps://indico
.math.cnrs.fr/event/3123/contributions/3185/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Couplings on Wiener space and a new version of Talagrand’s inequ
ality
DTSTART;VALUE=DATE-TIME:20180828T074000Z
DTEND;VALUE=DATE-TIME:20180828T082000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3186@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans Foellmer (Humboldt University Berlin)\nWe discu
ss adaptive and anticipating couplings on Wiener space. In particular we t
ake a fresh look at the connection between the Wasserstein metric and the
relative entropy with respect to Wiener measure provided by Talagrand’s
inequality and its extension to Wiener space by Feyel and Ustunel. Using r
esults of Nina Gantert for large deviations in the quadratic variation of
Brownian motion\, we extend this inequality beyond the absolutely continuo
us case\, using the notion of specific relative entropy.\n\nhttps://indico
.math.cnrs.fr/event/3123/contributions/3186/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On multisided optimal stopping problems for Levy processes
DTSTART;VALUE=DATE-TIME:20180829T092000Z
DTEND;VALUE=DATE-TIME:20180829T095000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3188@indico.math.cnrs.fr
DESCRIPTION:Speakers: Elena Boguslavskaya (Brunel University London)\nIn t
he last decades solving multisided optimal stopping problems was of intere
st.\n\nWe will show how to approach the above problems for Levy processes
if the payoff function is an exponential polynomial (possibly multidimensi
onal)\, and present several examples. The method we use is based on Appell
integral transform.\n\nhttps://indico.math.cnrs.fr/event/3123/contributio
ns/3188/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Entropie Minimal Martingale Measure for Lévy Processes
DTSTART;VALUE=DATE-TIME:20180831T092000Z
DTEND;VALUE=DATE-TIME:20180831T095000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3189@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hans-Jürgen Engelbert (Friedrich Schiller-Universit
y of Jena\, Institute of Mathematics)\nWe consider a geometric Lévy marke
t with asset price S t = S 0 exp(X t )\, where X is a\ngeneral Lévy proce
ss on (Ω\, F\, P)\, and interest rate equal to zero. As it is well known\
,\nexcept for the cases that X is a Brownian motion or a Poisson process\,
the market is\nincomplete. Therefore\, if the market is arbitrage-free\,
there are many equivalent mar-\ntingale measures and the problem arises to
choose an appropriate martingale measure\nfor pricing contingent claimes.
\nOne way is to choose the equivalent martingale measure Q ∗ which minim
izes the\nrelative entropie to P\, if it exists. Another choice is the fam
ous Esscher martingale\nmeasure Q E \, if it exists.\nThe main objective o
f the present talk is to discuss a simple and rigorous approach\nfor provi
ng the fact that the entropie minimal martingale measure Q ∗ and the Ess
cher\nmartingale measure Q E actually coincide: Q ∗ = Q E . Our method c
onsists of a suit-\nable approximation of the physical probability measure
P by Lévy preserving probaility\nmeasures P n.\nThe problem was treated
in several earlier papers but more heuristally or in a so-\nphisticated wa
y.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3189/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimal (financial) position targeting via decoupling fields
DTSTART;VALUE=DATE-TIME:20180831T130000Z
DTEND;VALUE=DATE-TIME:20180831T133000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3147@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stefan Ankirchner (University of Jena)\nIn the talk
we consider a variant of the basic problem of the calculus of variations\,
where the Lagrangian is convex and subject to randomness adapted to a Bro
wnian filtration. We solve the problem by reducing it\, via a limiting arg
ument\, to an unconstrained control problem that consists in finding an ab
solutely continuous process minimizing the expected sum of the Lagrangian
and the deviation of the terminal state from a given target position. Usin
g the Pontryagin maximum principle one can characterize a solution of the
unconstrained control problem in terms of a fully coupled forward-backward
stochastic differential equation (FBSDE). We use the method of decoupling
fields for proving that the FBSDE has a unique solution.\nThe talk is bas
ed on joint work with Alexander Fromm\, Thomas Kruse and Alexandre Popier.
\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3147/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On sets of laws of continuous martingales
DTSTART;VALUE=DATE-TIME:20180828T154000Z
DTEND;VALUE=DATE-TIME:20180828T161000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3191@indico.math.cnrs.fr
DESCRIPTION:Speakers: Youri Kabanov (Lomonosov Moscow State University and
Université de Bourgogne Franche-Comté)\nWe discuss relations between se
ts of laws of stochastic integrals with respect to a Wiener process \nand
general continuous martingales having quadratic characteristics whose RN-d
erivatives evolve in the \nsame convex set of positive semidefinite symmet
ric matrices.\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3191
/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Solution to the Time-Scale Fractional Puzzle in the Implied Vola
tility
DTSTART;VALUE=DATE-TIME:20180829T070000Z
DTEND;VALUE=DATE-TIME:20180829T074000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3192@indico.math.cnrs.fr
DESCRIPTION:Speakers: Masaaki Kijima (Tokyo Metropolitan University)\nIn t
he option pricing literature\, it is well known that (i) the decrease in t
he smile amplitude is much slower than the standard stochastic volatility
models and (ii) the term structure of the at-the-money volatility skew is
approximated by a power-law function with the exponent close to zero. Thes
e stylized facts cannot be captured by standard models and\, while (i) has
been explained by using a fractional volatility model with Hurst index $H
>1/2$\, (ii) is proved to be satisfied by a {\\it rough} volatility model
with $H<1/2$ under a risk-neutral measure. This paper provides a solution
to this fractional puzzle in the implied volatility. Namely\, we construct
a two-factor fractional volatility model and develop an approximation for
mula for European option prices. It is shown through numerical examples th
at our model can resolve the fractional puzzle\, when the correlations bet
ween the underlying asset process and the factors of rough volatility and
persistence belong to a certain range. More specifically\, depending on th
e three correlation values\, the implied volatility surface is classified
into four types: (1) the roughness exists\, but the persistence does not\;
(2) the persistence exists\, but the roughness does not\; (3) both the ro
ughness and the persistence exist\; and (4) neither\nthe roughness nor the
persistence exist. (Joint work with H. Funahashi)\n\nhttps://indico.math.
cnrs.fr/event/3123/contributions/3192/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Ruin Problem with Investment when the Risky Asset is a Semi
martingale
DTSTART;VALUE=DATE-TIME:20180831T095000Z
DTEND;VALUE=DATE-TIME:20180831T102000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3193@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jerome Spielmann (Universite d'Angers)\nIn this talk
\, we study the ruin problem with investment in a general framework where
the business part X is a Lévy process and the return on investment R is a
semimartingale. We obtain upper bounds on the finite and infinite time ru
in probabilities that decrease as a power function when the initial capita
l increases. When R is a Lévy process\, we retrieve the well-known result
s. Then\, we show that these bounds are asymptotically optimal in the fini
te time case\, under some simple conditions on the characteristics of X. F
inally\, we obtain a condition for ruin with probability one when X is a B
rownian motion with negative drift and express it explicitly using the cha
racteristics of R. (The results were obtained as a joint work with L. Vost
rikova.)\n\nhttps://indico.math.cnrs.fr/event/3123/contributions/3193/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Law of Large Numbers and Central Limit Theorem under Uncertainty o
f Probability Distributions
DTSTART;VALUE=DATE-TIME:20180829T120000Z
DTEND;VALUE=DATE-TIME:20180829T124000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3195@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shige Peng (Shandong University)\nHow to calculate t
he essential uncertainty of probability distributions hidden behind a real
data sequence is a theoretically and practically important challenging
problem.\n\nRecently some fundamentally important progresses have been ach
ieved in the domain of law of large numbers (LLN) and central limit theor
em (CLT) with a much weaker assumption of independence and identical distr
ibution (i.i.d.) under a sublinear expectation. \n\nThese new LLN and CTL
can be applied to a significantly wide classes of data sequence to constr
uct the corresponding optimal estimators. In particular\, many distributio
n uncertainties hidden behind data sequences are able to be quantitativel
y calculated by introducing a new algorithm of phi-max-mean type. \n\nI
n this talk\, I take some typical examples to provide a more concrete expl
anation of the above mentioned LLN and CLT\, the key idea of their proofs\
, as well as the new phi-max-mean estimators.\n\nhttps://indico.math.cnrs
.fr/event/3123/contributions/3195/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:On discrete Schur-constant vectors\, with applications.
DTSTART;VALUE=DATE-TIME:20180829T135000Z
DTEND;VALUE=DATE-TIME:20180829T142000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3223@indico.math.cnrs.fr
DESCRIPTION:Speakers: Stéphane Loisel (Université de Lyon 1)\nThis talk
is concerned with Schur-constant survival models for discrete random varia
bles. Our main purpose is to prove that the associated partial sum process
is a non- homogeneous Markov chain. This is shown in different cases as
the random variables take values in the set of nonnegative integers or in
the set of integers smaller than $m\\geq 1$. The property of Schur-constan
cy is also compared for thesecases. We also present a few additional resul
ts on Schur-constant vectors. This is based on joint works with Castaner\,
Claramunt\, Lefèvre and Utev.\n\nhttps://indico.math.cnrs.fr/event/3123/
contributions/3223/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3223/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Utility maximization for Lévy switching models
DTSTART;VALUE=DATE-TIME:20180828T143000Z
DTEND;VALUE=DATE-TIME:20180828T150000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3224@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yuchao Dong (University of Angers)\nThis article is
devoted to the maximization of HARA utilities of Lévy\nswitching process
on finite time interval via dual method. We give the description\nof all f
-divergence minimal martingale measures in progressively enlarged\nfiltrat
ion\, the expression of their Radon-Nikodym densities involving Hellinger\
nand Kulback-Leibler processes\, the expressions of the optimal strategies
for\nthe maximization of HARA utilities as well as the values of the corr
esponding\nmaximal expected utilities. The example of Brownian switching m
odels is presented.\n\nThis is common work with Lioudmila Vostrikova.\n\nh
ttps://indico.math.cnrs.fr/event/3123/contributions/3224/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3224/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Controlled mean-field dynamics in stochastic control problems depe
nding on the law of state process
DTSTART;VALUE=DATE-TIME:20180831T140000Z
DTEND;VALUE=DATE-TIME:20180831T143000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3201@indico.math.cnrs.fr
DESCRIPTION:Speakers: Rainer Buckdahn (Université de Bretagne Occidentale
)\nThe starting point of the talk is a recent work with Juan Li (Shandong
University\,\nWeihai\, P.R.China) and Jin Ma (University of South Californ
ia\, Los Angeles\, U.S.A.)\, “A mean-\nfield stochastic control problem
with partial observations” (Annals of Appl.Probability\, 2017: [1]) in\n
which we studied Pontryagin’s optimality principle for a stochastic cont
rol problem whose dynamics\nare given by the stochastic differential equat
ion (SDE)\nZ t\nZ t\nX|Y\nX t = x +\nb(s\, X .∧s \, μ s \, u s (Y ))ds
+\nσ(s\, X .∧s \, μ s X|Y \, u s (Y ))dB s 1 \,\n0\n0\nR t\nY t = 0 h(
s\, X s )ds + B t 2 \, t ∈ [0\, T ]\, P -a.s.\,\nwhere (B 1 \, B 2 ) is
a P -Brownian motion\, the controlled state process X is only observable t
hrough\nthe observation process Y and so the control process u = u(Y ) is
a non anticipating functional of\nthe observation process Y . Moreover\, u
nlike classical controlled dynamics\, the coefficients σ and b\ndo not on
ly depend on the paths of the controlled state process X and the control u
(Y ) but also\nX|Y\non the law μ s = P ◦ [E[X s |Y r \, r ≤ s]] −1
\, s ∈ [0\, T ]. Motivations for such a type of dynamics are\ngiven in [
1]. However\, in [1] the dependence of the law is linear\; the talk will s
tudy the case where\nthe coefficients are non linear functions of the law.
Moreover\, unlike in [1] the coefficients b and σ\nare only supposed to
be continuous in the law w.r.t. the 1-Wasserstein metric and on h we only\
nimpose boundedness and Lipschitz continuity in the state variable. The ma
in objective of the talk\nis to prove the weak existence and the uniquenes
s in law for the above dynamics.\n\nhttps://indico.math.cnrs.fr/event/3123
/contributions/3201/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lie group analysis of an optimization problem for a portfolio with
an illiquid asset
DTSTART;VALUE=DATE-TIME:20180828T123000Z
DTEND;VALUE=DATE-TIME:20180828T130000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3153@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ljudmila A. Bordag (University of Applied Sciences Z
ittau/Gorlitz)\nWorking in the Merton's optimal consumption framework wit
h continuous time we consider an optimization problem for a portfolio with
an illiquid\, a risky and a risk-free asset. Our goal in this paper is to
carry out a complete Lie group analysis of PDEs describing value function
and investment and consumption strategies for a portfolio with an illiqui
d asset that is sold in an exogenous random moment of time $T$ with a pres
cribed liquidation time distribution. The problem of such type leads to th
ree dimensional nonlinear Hamilton-Jacobi-Bellman (HJB) equations. Such eq
uations are not only tedious for analytical methods but are also quite cha
llenging form a numeric point of view. To reduce the three-dimensional pro
blem to a two-dimensional one or even to an ODE one usually uses some subs
titutions\, yet the methods used to find such substitutions are rarely dis
cussed by the authors.\n\nWe use two types of utility functions: general H
ARA type utility and logarithmic utility. We carry out the Lie group analy
sis of the both three dimensional PDEs and are able to obtain the admitted
symmetry algebras. Then we prove that the algebraic structure of the PDE
with logarithmic utility can be seen as a limit of the algebraic structure
of the PDE with HARA-utility as $\\gamma \\to 0$. Moreover\, this relatio
n does not depend on the form of the survival function $\\overline{\\Phi}
(t)$ of the random liquidation time $T$.\nWe find the admitted Lie algebra
for a broad class of liquidation time distributions in cases of HARA and
log utility functions and formulate corresponding theorems for all these c
ases.\n\nWe use found Lie algebras to obtain reductions of the studied equ
ations. Several of similar substitutions were used in other papers before
whereas others are new to our knowledge. This method gives us the possibil
ity to provide a complete set of non-equivalent substitutions and reduced
equations.\n\nWe also show that if and only if the liquidation time defin
ed by a survival function $\\overline{\\Phi} (t)$ is distributed exponent
ially\, then for both types of the utility functions we get an additional
symmetry. We prove that both Lie algebras admit this extension\, i.e. we o
btain the four dimensional $L^{HARA}_4$ and $L^{LOG}_4$ correspondingly fo
r the case of exponentially distributed liquidation time.\nWe list reduced
equations and corresponding optimal policies that tend to the classical M
erton policies as illiquidity becomes small.\n\n This research was support
ed by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Ag
reement Number 304617 (FP7 Marie Curie Action\, Project Multi-ITN STRIKE -
Novel Methods in Computational Finance)\n\nhttps://indico.math.cnrs.fr/ev
ent/3123/contributions/3153/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Recover Dynamic Utility from Monotonic Characteristic Processes
DTSTART;VALUE=DATE-TIME:20180828T120000Z
DTEND;VALUE=DATE-TIME:20180828T123000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3226@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nicole El Karoui ()\nIn the real world\, decision ma
king under uncertainty is often viewed as an opti-\nmization problem under
choice criterium\, and most of theory focuses on the deriva-\ntion of the
"optimal decision" and its out-comes. But\, poor information is available
\non the criterium yielding to these observed data. The interesting proble
m to infer\nthe unknown criterium from the known results is an example of
inverse problem.\nHere we are concerned with a very simple version of the
problem: what does ob-\nservation of the "optimal" out-put tell us about t
he preference\, expressed in terms\nof expected utility\; in Economics\, t
his question was pioneered by the american\neconomist Samuelson in1938.\nT
ypically we try to reproduce the properties of the stochastic value functi
on of\na portfolio optimization problem in finance\, which satisfies the f
irst order condi-\ntion U (t\, z)). In particular\, the utility process U
is a strictly concave stochastic\nfamily\, parametrized by a number z ∈
R + (z 7→ U (t\, z))\, and the characteris-\ntic process X c = (X t c (x
)) is a non negative monotonic process with respect to\nits initial condit
ion x\, satisfying the martingale condition U (t\, X t c (x)) is a martin-
\ngale\, with initial condition U (0\, x) = u(x). We first introduce the a
djoint process\nY t (u x (x)) = U x (t\, X t c (x)) which is a characteris
tic process for the Fenchel transform\nof U if and only if X t c (x)Y t (u
x (x)) is a martingale. The minimal property is the\nmartingale property
of Y t (u x (x)) with the x-derivative of X t c (x)\, which is sufficient\
nto reconstruct U from U x (t\, x) = Y t (u x ((X t c ) −1 (x))). Obviou
sly\, in general\, with-\nout additional constraints\, the characterizatio
n is not unique. Various example are\ngiven\, in general motivated by fina
nce or economics: contraints on a characteristic\nportfolio in a economy a
t the equilibrium\, thoptimal portfolio for a in complete\nfinancial marke
t\, under strongly orthogonality between X and Y \, the mixture of\ndiffer
ent economies....In any case\, the results hold for general but monotonic
pro-\ncesses\, without semimartingale assumptions.\n\nhttps://indico.math.
cnrs.fr/event/3123/contributions/3226/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3226/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Decomposition of random times\, application to default times
DTSTART;VALUE=DATE-TIME:20180828T130000Z
DTEND;VALUE=DATE-TIME:20180828T133000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3183@indico.math.cnrs.fr
DESCRIPTION:Speakers: Monique Jeanblanc (université Evry Val d'ESSONNE)\n
We provide a general model of default time\, extending the models of Jiao
and\nLi (modelling sovereign risks) and Gehmlich and Schmidt (dynamic defa
ultable\nterm structure modelling beyond intensity paradigm).\nWe show tha
t any random time τ can be decomposed in two parts as τ = τ 1 ∧τ 2\n
under the condition that the first random time τ 1 avoids stopping times
in the ref-\nerence filtration F\, and the second time τ 2 is thin\, i.e.
\, its graph is included in a\ncountable union of graphs of stopping times
in the reference filtration F. Under the\ncondition τ 1 ∨ τ 2 = ∞\,
the decomposition is unique. This decomposition is based\non a study of t
he dual optional projection of τ \, as the decomposition of a stopping\nt
ime into accessible and totally inaccessible is based on the dual predicta
ble pro-\njection. We show that for a thin time τ 2 \, any F-martingale i
s a semimartingale in\nits progressive enlargement with τ 2 and we give i
ts semimartingale decomposition.\nWe prove that any martingale in the refe
rence filtration is a semimartingale in\nthe progressive enlargement with
τ if and only if the same property holds for the\nprogressive enlargement
with τ 1 and we give its semimartingale representation.\nWe establish in
that the immersion property holds for τ if and only if it holds\nfor τ
1 .This is a joint work with Anna Aksamit and Tahir Choulli.\n\nhttps://i
ndico.math.cnrs.fr/event/3123/contributions/3183/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some sequential problems for Brownian motion with random drift in
statistics and finance.
DTSTART;VALUE=DATE-TIME:20180828T070000Z
DTEND;VALUE=DATE-TIME:20180828T074000Z
DTSTAMP;VALUE=DATE-TIME:20200807T161658Z
UID:indico-contribution-3123-3187@indico.math.cnrs.fr
DESCRIPTION:Speakers: Albert Shiryaev (Steklov Mathematical Institute)\nWe
consider two models of observable process X = (X t ):\nModel A: X t = μt
+ B t \,\nModel B: X t = μt + ν(t − θ)^+ + B t \,\nwhere B = (B t )
is a standard Brownian motion\, μ and ν are unknown parameters\,\nand θ
is a disorder time.\nFor Model A\, we consider some sequential statistica
l problems with different\nrisk functions.\nFor Model B\, we deal with seq
uential problems of the following type:\nH 1 = sup EX τ\nor H 2 = sup EE(
X τ )\,\nτ ≤1\nτ ≤1\nwhere τ is a stopping time. We show that for
such functionals H 1 and H 2 optimal\nstopping times have the following fo
rm:\nτ ∗ = inf{t ≤ 1: ψ(t) ≥ a ∗ (t)}\,\nwhere ψ(t) is some sta
tistic of observations and a ∗ (t) is a curvilinear boundary\nsatisfying
the Fredholm integral equation of second order. These problems will\nbe a
pplied to the real asset price models (Apple\, Nasdaq).\nThe talk will giv
es a survey of the joint papers of authors with Četin\,\nNovikov\, Zhitlu
khin\, and Muravlev.\n\nhttps://indico.math.cnrs.fr/event/3123/contributio
ns/3187/
LOCATION:Angers - France
URL:https://indico.math.cnrs.fr/event/3123/contributions/3187/
END:VEVENT
END:VCALENDAR